$$\int \frac{\sin 2 x}{(1+\sin x)(2+\sin x)} d x=a \log |1+\sin x|-b \log |2+\sin x|+c$$ then the value of $a$ and $b$ is ----------------

$\int\left(e^{x \log _e 6}\right) e^x d x=\phi(x)+c$ then $\phi(x)=$

$\int \frac{\sin x+\cos x}{\sqrt{1+2 \sin x \cos x}} d x=\varphi(x)+C$ Then $\varphi(x)=$

$\int \frac{e^{\tan ^{-1} x}}{\left(1+x^2\right)}\left(1+x+x^2\right) d x=$